SOLUTION: Create your own quadratic equation that cannot be solved by factoring, but can be solved using the quadratic formula. Identify the values of a, b, and c, and find the solutions usi

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Create your own quadratic equation that cannot be solved by factoring, but can be solved using the quadratic formula. Identify the values of a, b, and c, and find the solutions usi      Log On


   

Question 329177: Create your own quadratic equation that cannot be solved by factoring, but can be solved using the quadratic formula. Identify the values of a, b, and c, and find the solutions using the quadratic formula. Show all work to receive credit.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The way to attack this one is to use the idea that if is a zero of of a polynomial function, then must be a factor of the polynomial. Further we know that irrational roots of polynomial equations always come in conjugate pairs.

So, let's say that



is a root of our quadratic equation. From that we can determine two things. First:



is the other zero of the function and the factors of the quadratic trinomial are:



Which, in order to be a quadratic equation in standard form, must be multiplied using FOIL and set equal to zero.



Now you have a quadratic equation in standard form, where

, , and

You can leave your answer like that, or pick a couple of numbers to substitute for and . Pick any numbers you like as long as is NOT a perfect square. (If you pick a perfect square for , then your quadratic will turn out to be factorable)

John